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CONORBIT: constrained optimization by radial basis function interpolation in trust regions

Journal Article · · Optimization Methods and Software
 [1];  [2]
  1. Saint Joseph's Univ., Philadelphia, PA (United States)
  2. Argonne National Lab. (ANL), Argonne, IL (United States)
+ Show Author Affiliations
Here, this paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, a chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA, a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.
Research Organization:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Grant/Contract Number:
AC02-06CH11357
OSTI ID:
1373699
Journal Information:
Optimization Methods and Software, Journal Name: Optimization Methods and Software Journal Issue: 3 Vol. 32; ISSN 1055-6788
Publisher:
Taylor & FrancisCopyright Statement
Country of Publication:
United States
Language:
English

References (38)

Convex Analysis and Nonlinear Optimization book January 2006
Convex Analysis and Nonlinear Optimization book January 2000
A rigorous framework for optimization of expensive functions by surrogates journal February 1999
Recent progress in unconstrained nonlinear optimization without derivatives journal October 1997
A rigorous framework for optimization of expensive functions by surrogates journal January 1999
Geometry of interpolation sets in derivative free optimization journal December 2006
Nonlinear programming without a penalty function journal January 2002
Benchmarking optimization software with performance profiles journal January 2002
UOBYQA: unconstrained optimization by quadratic approximation journal May 2002
Nonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search journal October 2007
A quasi-multistart framework for global optimization of expensive functions using response surface models journal June 2012
Optimizing radial basis functions by d.c. programming and its use in direct search for global derivative-free optimization journal June 2011
A novel reverse flow strategy for ethylbenzene dehydrogenation in a packed-bed reactor journal December 1994
Stochastic radial basis function algorithms for large-scale optimization involving expensive black-box objective and constraint functions journal May 2011
Constrained optimization involving expensive function evaluations: A sequential approach journal January 2005
Multi-objective optimization of tumor response to drug release from vasculature-bound nanoparticles journal May 2020
Modeling an Augmented Lagrangian for Blackbox Constrained Optimization journal January 2016
Boosters: A Derivative-Free Algorithm Based on Radial Basis Functions journal January 2009
Constrained optimization by radial basis function interpolation for high-dimensional expensive black-box problems with infeasible initial points journal February 2013
Use of quadratic models with mesh-adaptive direct search for constrained black box optimization journal February 2013
A Simplex Method for Function Minimization journal January 1965
Mesh Adaptive Direct Search Algorithms for Constrained Optimization journal January 2006
Using Sampling and Simplex Derivatives in Pattern Search Methods journal January 2007
ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions journal January 2008
A Progressive Barrier for Derivative-Free Nonlinear Programming journal January 2009
A Globally Convergent Augmented Lagrangian Algorithm for Optimization with General Constraints and Simple Bounds journal April 1991
Benchmarking Derivative-Free Optimization Algorithms journal January 2009
Global Convergence of Radial Basis Function Trust Region Derivative-Free Algorithms journal July 2011
Sequential Penalty Derivative-Free Methods for Nonlinear Constrained Optimization journal January 2010
Introduction to Derivative-Free Optimization book January 2009
A Linesearch-Based Derivative-Free Approach for Nonsmooth Constrained Optimization journal January 2014
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods journal January 2003
On the Convergence of Pattern Search Algorithms journal February 1997
Algorithm 909: NOMAD: Nonlinear Optimization with the MADS Algorithm journal February 2011
Boosters: a Derivative-Free Algorithm Based on Radial Basis Functions journal January 2009
Benchmarking Optimization Software with Performance Profiles text January 2001
Modeling an Augmented Lagrangian for Blackbox Constrained Optimization text January 2016
Modeling an Augmented Lagrangian for Blackbox Constrained Optimization text January 2015

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A Survey of Surrogate Approaches for Expensive Constrained Black-Box Optimization book June 2019
Best practices for comparing optimization algorithms journal September 2017
Efficient global optimization for high-dimensional constrained problems by using the Kriging models combined with the partial least squares method journal February 2018
Best practices for comparing optimization algorithms. text January 2019
Best practices for comparing optimization algorithms text January 2017
Efficient global optimization for high-dimensional constrained problems by using the Kriging models combined with the partial least squares method text January 2018
Efficient global optimization for high-dimensional constrained problems by using the Kriging models combined with the partial least squares method text January 2018

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97 MATHEMATICS AND COMPUTING
black-box optimization
computationally expensive function
constrained optimization
fully linear model
radial basis function interpolation
simulation-based optimization
trust region